Calculus of Variations and Geometric Measure Theory

A. Figalli - D. Jerison

How to recognize convexity of a set from its marginals

created by figalli on 29 May 2013


Accepted Paper

Inserted: 29 may 2013
Last Updated: 29 may 2013

Journal: J. Funct. Anal.
Year: 2013


We investigate the regularity of the marginals onto hyperplanes for sets of finite perimeter. We prove, in particular, that if a set of finite perimeter has log-concave marginals onto a.e. hyperplane then the set is convex. Our proof relies on measuring the perimeter of a set through a Hilbertian fractional Sobolev norm, a fact that we believe has its own interest.